Rewrite as a simplified fraction. ${1.8\overline{5} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 185.5555...\\ 10x &= 18.5555...\end{align*}}$ Subtracting the two equations, we have: ${90x = 167}$ ${x = \dfrac{167}{90}} \text{or} {1 \dfrac{77}{90}}$